For Maths (all boards in England) you can re-sit as many/as few of the units you've already taken and your better/best attempt at each unit is the one that will count in calculating the overall grade.
For Chemistry (all boards in England) you can carry forward the practical endorsement but have to re-sit all 3 written exams andthe grade will be based on how you do in this latest attempt.
If you want to take AS Further Maths then I think you will be OK taking the old spec as you have already taken Maths units, but it would be best to check with Edexcel - email them so you have it in writing. However, I'd advise against taking FP1, FP2 and FP3 as your AS Further Maths units - FP2 and FP3 are significantly harder than other units and you will be at a disadvantage compared to students who have done (say) FP1, S2 and D1